Historically, scientists and researchers have been faced with a problem when looking at visualisations of large amounts of data, of whether the patterns they are seeing are statistically valid or random.
Qlucore Projection Score is a unique functionality within Qlucore Omics Explorer that provides scientists and researchers with information on how accurately the visual representation is actually portraying data.
The Qlucore Projection Score technique is the brain child of Qlucore cofounder Magnus Fontes. It allows detailed comparison of representations obtained by principle component analysis (PCA) corresponding to different variable subsets, such as those obtained by variance filtering of a large data set.
The goal of exploratory visualisation is to find a representation from which interpretable and potentially interesting information can be extracted, that is, one that contains structures and patterns that are likely to be non-random. By following the evolution of the projection score in real time during variance filtering, the user can easily find the variable subset (and thus implicitly the variance cut-off) giving the most informative representation.
Magnus Fontes, the cofounder of Qlucore and developer of the Projection Score concept comments: “Qlucore is proud to be at the forefront of visualisation technology for scientific research. The Projection Score technique is one which I have been working on for a considerable time and it will be very valuable in aiding research scientists to validate their data visualisation work. The technique has been welcomed by my peers and I am delighted that it is now available on a commercial basis.”
To compute the projection score for a given data set, the user must start by computing the fraction of the total variance that is captured by the first three principal components. Then, an estimate is taken for the expected value of the same entity for completely random data.
The projection score is defined as the difference between the square root of the observed quantity and the square root of the expected value for random data. Hence, a large value of the projection score means that the PCA representation of the observed representation contains much more information (variance) than the corresponding representation of a random data set of the same size, which suggests that there are non-random, potentially interesting structures present in the representation.
In contrast, a projection score close to zero indicates that the representation is not more informative than one of a random data set and that there are no broad, consistent patterns to be found by the PCA.
By monitoring the evolution of the projection score during variance filtering, the optimal variable subset can be found. In Qlucore Omics Explorer the projection score is colored according to the displayed value. Red indicates a low projection score, yellow indicates a medium-high score and green corresponds to a high projection score.
In practice, almost all real data sets contain some non-random structure, and therefore it is very uncommon to get a projection score close to zero. The colors, and thus the boundaries between what is considered to be a “good” or a “bad” projection score, are based on our experience from applying the projection score to many different data sets, and should be interpreted mainly as rough guidelines suggesting the quality of the representations.
The projection score is a widely versatile technique that is applicable for a broad family of different statistical analyses. The statistical and technical details have been published by Magnus Fontes and Charlotte Soneson in the prestigous scientific journal BMC Bioinformatics in 2011.